NOC:Introduction to Rings and Fields

Lecture 1 - Introduction, main definitions

Lecture 2 - Examples of rings

Lecture 3 - More examples

Lecture 4 - Polynomial Rings - 1

Lecture 5 - Polynomial Rings - 2

Lecture 6 - Homomorphisms

Lecture 7 - Kernels, ideals

Lecture 8 - Problems - 1

Lecture 9 - Problems - 2

Lecture 10 - Problems - 3

Lecture 11 - Quotient Rings

Lecture 12 - First isomorphism and correspondence theorems

Lecture 13 - Examples of correspondence theorem

Lecture 14 - Prime ideals

Lecture 15 - Maximal ideals, integral domains

Lecture 16 - Existence of maximal ideals

Lecture 17 - Problems - 4

Lecture 18 - Problems - 5

Lecture 19 - Problems - 6

Lecture 20 - Field of fractions, Noetherian rings - 1

Lecture 21 - Noetherian rings - 2

Lecture 22 - Hilbert Basis Theorem

Lecture 23 - Irreducible, prime elements

Lecture 24 - Irreducible, prime elements, GCD

Lecture 25 - Principal Ideal Domains

Lecture 26 - Unique Factorization Domains - 1

Lecture 27 - Unique Factorization Domains - 2

Lecture 28 - Gauss Lemma

Lecture 29 - Z[X] is a UFD

Lecture 30 - Eisenstein criterion and Problems - 7

Lecture 31 - Problems - 8

Lecture 32 - Problems - 9

Lecture 33 - Field extensions - 1

Lecture 34 - Field extensions - 2

Lecture 35 - Degree of a field extension - 1

Lecture 36 - Degree of a field extension - 2

Lecture 37 - Algebraic elements form a field

Lecture 38 - Field homomorphisms

Lecture 39 - Splitting fields

Lecture 40 - Finite fields - 1

Lecture 41 - Finite fields - 2

Lecture 42 - Finite fields - 3

Lecture 43 - Problems - 10

Lecture 44 - Problems - 11